A dimension is a measurement of space. In a three-dimensional world, we usually think of three different directions as we measure the space in which we exist—length, width, and height. To indicate a certain location in space, we would provide three different coordinates on three different axes (x, y, and z).

The understanding of different dimensions is crucial in understanding much of mathematics. The ability to visualize and a flexibility in adjusting to n-dimensional worlds is a skill worth pursuing.

Portraying Three Dimensions

Even though most everyday experience is in three dimensions, most high school mathematics takes place in a two-dimensional world in which there is only length and width. Part of this is because traditional learning is largely communicated through books or on a chalkboard. Book pages or the planes of chalkboards have primarily two dimensions. Even if there is a picture in a book...